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Error bounds in the gap metric for dissipative balanced approximations (2013)
Journal Article
Guiver, C., & Opmeer, M. R. (2013). Error bounds in the gap metric for dissipative balanced approximations. Linear Algebra and its Applications, 439(12), 3659-3698. https://doi.org/10.1016/j.laa.2013.09.032

We derive an error bound in the gap metric for positive real balanced truncation and positive real singular perturbation approximation. We prove these results by working in the context of dissipative driving-variable systems, as in behavioral and sta... Read More about Error bounds in the gap metric for dissipative balanced approximations.

Bounded real and positive real balanced truncation for infinite-dimensional systems (2013)
Journal Article
Guiver, C., & Opmeer, M. R. (2013). Bounded real and positive real balanced truncation for infinite-dimensional systems. Mathematical Control and Related Fields, 3(1), 83-119. https://doi.org/10.3934/mcrf.2013.3.83

Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional case in terms of the bo... Read More about Bounded real and positive real balanced truncation for infinite-dimensional systems.

Model Reduction by Balanced Truncation (2012)
Thesis
Guiver, C. (2012). Model Reduction by Balanced Truncation. (Thesis). University of Bath. http://researchrepository.napier.ac.uk/Output/4181395

Model reduction by balanced truncation for bounded real and positive real input-stateoutputsystems, known as bounded real balanced truncation and positive real balancedtruncation respectively, is addressed. Results for finite-dimensional systems were... Read More about Model Reduction by Balanced Truncation.

A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds” (2011)
Journal Article
Guiver, C., & Opmeer, M. R. (2011). A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds”. IEEE Transactions on Circuits and Systems I: Regular Papers, 58(6), 1410-1411. https://doi.org/10.1109/tcsi.2010.2097750

We provide a counter example to the H∞ error bound for the difference of a positive real transfer function and its positive real balanced truncation stated in “Positive realness preserving model reduction with H-\infty norm error bounds” IEEE Trans.... Read More about A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds”.

Non-dissipative boundary feedback for elastic beams (2010)
Presentation / Conference Contribution
Guiver, C., & Opmeer, M. R. (2010, July). Non-dissipative boundary feedback for elastic beams. Presented at 19th International Symposium on Mathematical Theory of Networks and Systems, Budapest, Hungary

We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenkobeam unstable.